We examine the activity detection performance and the channel estimation accuracy of the proposed algorithm through computer simulations. As a reference, we compare the proposed FAT-DL algorithm with the AMP algorithm [1]}, the LAMP algorithm [2]}, the LVAMP algorithm [2]}, the FISTA algorithm [4]}, and the OMP algorithm [5]}. We use the activity error rate (AER) to measure the detection performance and normalized mean square error (NMSE) to measure the channel estimation accuracy. The AER is a sum of the miss detection probability, defined as the probability that a device is active but is declared to be inactive, and the false-alarm probability, defined as the probability that a device is inactive but the detector declares it to be active. The NMSE of all active devices is defined as \(10\log _{10}\frac{\left\Vert  \hat{\mathbf {X}}_{\mathcal {K}}-\mathbf {X}_{\mathcal {K}} \right\Vert _F^2}{\left\Vert  \mathbf {X}_{\mathcal {K}} \right\Vert _F^2}\)  where \(\mathbf {X}_{\mathcal {K}}\)  collects the row vectors corresponding to the active support \(\mathcal {K}\)  in \(\mathbf {X}\) . The SNR is defined as \(10\log _{10}(\left\Vert \mathbf {AX}\right\Vert _F^2/{LM\sigma ^2})\) .
